What is the purpose of the "gamma" parameter in SVMs?
I've summarized the key ideas of SVMs. So this is how $\gamma$ is used with a gaussian Kernel:

$$K_{\text{Gauss}}(\mathbf{x}_i, \mathbf{x}_j) = e^{\frac{-\gamma\|\mathbf{x}_i - \mathbf{x}_j\|^2}{2 \sigma^2}}$$

The bigger the $\gamma$, the more "linear" the decision boundary will be. The closer to 0, the more support vectors you have/the more non-linear the boundary is (see interactive example)

You can also find it on udacity: SVM Gamma Parameter

In practice, you can use a grid search or random search to get good values.